PPGMAT/CCET

Inequalities for eigenvalues of fourth-order elliptic operators in divergence form on complete Riemannian manifolds

Marcio Costa Araujo Filho

Abstract:

In this presentation, we will describe some inequalities of Payne–P´olya– Weinberger–Yang type for eigenvalues of fourth-order elliptic operators in weighted divergence form on complete Riemannian manifolds which generalizes the corresponding result for the clamped plate problem. We also present estimates for lower-order eigenvalues that contain some of the estimates from the literature. As an application of our results, we obtain eigenvalues estimates for the bi-drifted Cheng-Yau operator. To finish, let us talk about recent perspectives on this subject in pinched Cartan-Hadamard manifolds.